Environ. Sci. Technol. 1991, 2 5 , 468-474
Kinetics and Mechanism of Formation of Chlorate Ion from the Hypochlorous Acid/Chlorite Ion Reaction at pH 6-10
Gilbert Gordon * and Satoshi Tachiyashlkit
Department of Chemistry, Miami University, Oxford, Ohio 45056
The reaction between free chlorine (HOCl/OCl-) and chlorite ion (C102-) has been studied in the p H 6.4-10.0 region. The reaction proceeds through the C1202 inter- mediate followed by a direct reaction of the intermediate with hypochlorous acid to form chlorate ion. Time-con- centration profiles were measured for each chlorine species, resulting in both total chlorine and redox balance. Neg- ligibly small amounts of chlorine dioxide are formed above pH 7. Indirect evidence suggests that, in this p H region, the formation of any chlorine dioxide is primarily due to the presence of concentration gradients or because of the adventitious presence of catalytic metal ion impurities.
Details of the overall reaction mechanism for the formation of chlorate ion are presented.
Introduction
Chlorine dioxide is a strong oxidant and a good biocide, which is considered to be an excellent alternative to chlorine for the disinfection of drinking water and wastewater (1-5). Chlorine dioxide (ClO,) is also known to significantly reduce odor and color in finished water.
However, the major disadvantage (6) of chlorine dioxide has been the potential hazards of the resulting inorganic byproducts, chlorite ion (C102-) and chlorate ion (C103-).
Typically, chlorine dioxide is used a t a concentration level between 0.1 and 2.0 mg/L for water treatment.
Frequently, the chlorine dioxide treatment is followed by an added dose of free chlorine. For many years, the origin of the chlorate ion was ascribed to a side reaction occurring during the formation of chlorine dioxide (7-13):
(1) (2) However, in the near-neutral pH region, the dispro- (3) results in the rapid conversion of chlorine to hypochlorous acid. The equilibrium constant for reaction 3 is 3.98 X (14, 15). Thus, when dissolved free chlorine is considered, the predominant chlorine species present in the pH 1-3 region is chlorine (C12), whereas hypochlorous acid pre- dominates in the pH 5-7 region and hypochlorite ion is the major species present above pH 8.
Recent investigations have suggested that the direct reaction of hypochlorous acid with chlorite ion could be responsible for the formation of chlorate ion (5,13,17-19) or that the formation of chlorine dioxide at higher pH levels may be due to the presence of trace metal ions ( 5 , 13-1 7, 20, 21). Various experimental limitations have made it difficult to measure the individual concentrations of each species such that a detailed mechanism could be proposed for the formation of chlorine dioxide and chlorate ion over the total pH region of interest (i.e., pH 2-10). The
2HC102
+
C1,-
2C102+
2H++
2C1-HClOz
+
Clz-
C103-+
H++
2C1-portionation reaction of chlorine
C12
+
H 2 0-
HOCl+
C1-+
H +On leave from Kagawa Nutrition College, Sakado, Saitama 350- 02, Japan.
purpose of this paper is (1) to provide such a detailed study by reporting the concentrations of each species as a function of time, thus obtaining a check on the total chlorine species balance and the redox balance; and (2) to propose a detailed mechanistic model for the reaction of chlorite ion/chlorous acid with free chlorine in the pH 6-10 region.
Experimental Section
Materials. Technical grade sodium chlorite (roughly 75% NaC10,; Kodak) was recrystallized three times from aqueous solution below 40 "C under minimal red light to remove impurities of sodium chloride (13.3%), sodium hypochlorite (10.5%), sodium chlorate (1.2%), and various trace-metal ions. The crystals of NaC1O2.3H2O thus ob- tained were dried over P4OlO in a desiccator. Iodometric analysis (9-13) of the resulting anhydrous NaClO, showed greater than 99% sodium chlorite, 0.23% sodium chloride, and less than 0.01% sodium chlorate. The total trace- metal ion content was less than 0.0015% as determined by atomic absorption spectroscopy.
Sodium hypochlorite was prepared by the method of Cady (22). Chlorine dissolved in carbon tetrachloride was allowed to react with the yellow form of mercuric oxide to produce chlorine monoxide. The carbon tetrachloride solution was shaken with an ice-cold 1 N sodium hydroxide solution to obtain an aqueous solution of sodium hypo- chlorite. The solution was acidified with H2S04 and hy- pochlorous acid was distilled under reduced pressure over solid Ag,SO,. The distillate was stored in the dark a t 0
"C. Working solutions of sodium hypochlorite were ob- tained by adding exact amounts of NaOH to the distillate.
This solution, as well as the sodium chlorite solution, was freshly prepared for each experiment and each solution was standardized iodometrically (13, 23-27). The excess sodium hydroxide in the sodium hypochlorite solution was calculated from the amount of NaOH added and the NaOCl concentration.
Since stock solutions of sodium hypochlorite and sodium chlorite were used to prepare working buffered solutions at each pH, initial concentrations and concentration ratios of these species are expressed as [NaOCl], and [NaC10210, respectively. In this context, it should be noted that the actual concentrations of the species HOCl and OC1- are determined by the initial concentration of sodium chlorite, [NaOCl],, and the pH of the solution.
Sodium perchlorate was synthesized from anhydrous sodium carbonate (Alfa Primary Standard) and perchloric acid (Fisher Reagent ACS Grade) and recrystallized three times from triply distilled water. Analytical reagent grade monosodium dihydrogen phosphate, disodium mono- hydrogen phosphate, trisodium phosphate (Mallinckrodt), sodium chloride (Fisher), and other chemicals of ACS Reagent Grade were used without further purification.
The preparation and standardization of the aqueous sodium thiosulfate solution (0.01 N) and the silver nitrate solution (0.003 N) in 70% methanol and the preparation of the osmium tetraoxide solution (0.03% in 2 N HzS04 solution) and 0.4 N As(II1) solution are described elsewhere (23).
468 Environ. Sci. Technol., Vol. 25, No. 3, 1991 0013-936X/91/0925-0468$02.50/0 0 199 1 American Chemical Society
Instruments. A Metrohm Herisau Model E 536 PO- tentiograph, a Metrohm Herisau Model E 535 autoburet, and an Orion Model 96-17 combination ion selective electrode were used for the argentometric potentiometric titrations. A Radiometer P H M 64 digital p H meter was used for p H measurements.
Procedures. A modification of the method described by Tang and Gordon (13) was used for the analysis of the reactants and products. A 50-mL syringe vessel (Le., a shrinking bottle) with a water jacket (25.0 "C) was used as a reaction vessel (28) throughout this study. The use of the vessel made it possible to remove any air gap above the sample, thus avoiding any loss of volatile chlorine dioxide produced during the reaction.
The reaction was carried out a t 25.0 "C in a 0.1 M phosphate buffer solution (pH 6.4-10.0), a t an ionic strength of 1.0 M adjusted by NaClO,. Initial concen- trations of the reactants [NaOCl],/ [NaC10210 were used in the ratios (mM/mM) 3/6, 6/3, 3/3, and 1/1. At the beginning of each experiment, the reaction syringe was clamped in an inverted position and exact volumes of the following solutions were delivered in order to the syringe by utilizing Silverman delivery syringes (29): phosphate buffer, sodium perchlorate, sodium hypochlorite, perchloric acid (to neutralize excess sodium hydroxide in the sodium hypochlorite solution), and sodium chlorite. Any air gap inside the vessel was quickly removed and the syringe was inverted and tightly sealed with a Teflon cap for the course of the reaction. No chlorine dioxide loss was observed during the reaction. The solution in the reaction syringe was well mixed by a Teflon stirring bar inside the syringe.
The syringe was covered with a black plastic bag to shade the reaction from light during the course of each experi- ment.
An aliquot of solution in the reaction syringe was transferred directly to a Silverman syringe (0.9180 f 0.0001 mL) via a plastic adaptor; thus, no chlorine dioxide was lost during the transferring process, and no air gap was formed in the reaction syringe after the sample had been transferred. Five aliquots of the sample solution were used to analyze the concentration of the reactants and the products a t specific times. Three aliquots were used for the iodometric titrations (samples 1-3) and the remaining two (samples 4 and 5 ) were used for the potentiometric argentometric titrations. The samples were treated as described below:
(1) An aliquot of the sample from the reaction syringe was introduced to the bottom of the titration vessel con- taining 10 mL of an 0.1 M KI solution. The solution was acidified to pH 2.0 by adding 2 M hydrochloric acid. The iodine formed was titrated with standard sodium thio- sulfate solution by using Thyodene as the end-point in- dicator. This titration value (A) equals the sum total normality of chlorine dioxide, chlorite ion, and hypo- chlorous acid.
(2) Another aliquot of the reaction was added to 10 mL of a 0.2 M Na211P04 solution (pH 9.0). The solution was bubbled with prepurified nitrogen gas for 10 min to elim- inate chlorine dioxide, and then 0.5 mL of a 2 M KI so- lution was instantaneously added to the solution with vigorous stirring. About 0.5 mL of a 2 M NaH2P0, solu- tion was added to adjust the solution to p H 7.0 and the iodine formed was titrated with thiosulfate solution. This titration value ( B ) amounts to the normality of hypo- chlorous acid/ hypochlorite ion. After the titration, the solution was adjusted to p H 2.0 by adding 2 M HC1 and the iodine produced was again titrated to give the nor- mality of chlorite ion (C). Subtraction of the B and C
titration values from the first titration value (A) results in the normality of chlorine dioxide.
(3) The third aliquot was introduced to 3 mL of water containing 10 mg of potassium iodide. The solution was adjusted to pH 2.0 by the addition of 2 M HC1. Then, 2 mL of hexane was added and the iodine produced was titrated with sodium thiosulfate solution with vigorous stirring until the hexane layer on the aqueous solution turned colorless. This titration effectively removes all of the chlorine dioxide and free chlorine (Le., Clz and hypo- chlorous acid/hypochlorite ion (HOCl/OCl-)).
After the solution was bubbled for 10 min with prepu- rified nitrogen the solution was shielded by an additional 2-mL layer of hexane in order to minimize the atmospheric oxygen/iodide ion reaction to produce iodine. In addition, for the determination of chlorate ion, a special closed ti- trating system was used in order to minimize atmospheric oxygen contamination. Specifically, this closed titrating system allowed for degassing of the sample solution (in- cluding the concentrated HC1 and the saturated Na2HP04 buffer) and provided protection to the solutions from at- mospheric oxygen during the course of the reactions and during the subsequent titrations.
Next, 5 mL of degassed, concentrated hydrochloric acid was added to the solution to produce iodine. The solution was allowed to react for 20 min. This was followed by the addition of 10 mL of a degassed, saturated Na2HP04 so- lution in order to partially neutralize the high concentra- tion of HCl. The resulting solution was titrated imme- diately with vigorous stirring under a nitrogen atmosphere until the reddish purple color of the hexane layer disap- peared. The titration volume corresponds directly to the normality of chlorate ion.
(4) For determination of the concentration of chloride ion, an aliquot of the reaction sample was added to 20 mL of a 70% aqueous methanol solution containing 0.3 mL of 2 M acetic acid. The solution was titrated with 0.003 M silver nitrate in 70% methanol solution. The end point was determined potentiometrically with a chloride ion selective electrode (23).
(5) The fifth aliquot was used for the analysis of the total chlorine concentration of the reaction sample. The sample aliquot and 0.5 mL of the osmium tetraoxide catalyst (0.1% OsO, in water) were added to 20 mL of a 70%
methanol solution containing 0.25 mL of 0.4 N As(III), and the resulting solution was stirred for
-
1 s. After a 20-min reaction period, the chloride ion formed was titrated po- tentiometrically with silver nitrate in 70% methanol (23).The titration value corresponds to the total chlorine.
By means of statistical analysis of repeated measure- ments of the same sample, the precision of the individual iodometric analyses were shown to be f0.04 mN (f0.0035 mL) and f0.02 mM (f0.006 mL) for the individual ar- gentometric analyses.
Results
The concentrations of the reactants and the products were determined as a function of time in various experi- ments in the pH 6.4-10.0 range with the initial concen- trations of reactants of [NaOCl],/ [NaClO,], (mM/mM) a t 316,613,313, and
111.
Typical examples of such de- terminations are shown in Figure l and in Table I. The agreement between oxygen and chlorine balances a t the beginning and during the course of the reaction was better than f 1 % , as can be seen from the results given in Table I.Stoichiometry of the Reaction. The stoichiometry of the reaction between HOCl/OCl- and C102- was derived by analyzing the changes in the concentrations of the
100 7
3
0"
E i,
v
2
0 10 20 30 40 (hours)
Time
Figure 1. Concentrations of reactants and products in the HOCI/CIO,- reaction as a function of time at pH 8.82 with [NaOCI],/[NaCIO,], = 6 mM/3 mM.
Table I. Typical Reaction Data for the Hypochlorous AcidKhlorite Ion Reaction with Phosphate Buffer at 1.00 M Ionic Strength Maintained with Sodium Perchlorate
(A) [NaOC1],/[NaCIO,]o = 1.00, pH 6.38 time, HOCI, ClOc, C102, C1-, ClO,-,
min mM mM mM mM mM
0.0 1.04 1.04 0.00 0.00 0.00
9.0 0.44 0.49 0.18 0.56 0.42 13.0 0.33 0.42 0.19 0.65 0.49
17.5 0.33 0.37 0.16 0.67 0.55
21.0 0.26 0.33 0.17 0.73 0.59 35.5 0.22 0.25 0.15 0.79 0.68
70.6 0.11 0.19 0.14 0.89 0.77
130.5 0.10 0.11 0.12 0.92 0.83 (B) [NaOC1],/[NaCIO,]o = 1.95, pH 8.82 time, HOCI, C102-, C102, C1-, C103-.
h mM mM mM mM mM
0.0 5.87 3.01 0.00 0.00 0.00
0.7 4.99 2.27 0.12 0.81 0.63
2.5 4.47 1.73 0.10 1.34 1.23
5.5 3.93 1.18 0.07 1.89 1.89
10.4 3.62 0.70 0.05 2.33 2.30
21.1 2.97 0.095 2.72
23.9 2.94 0.22 0.08 2.87
46.1 2.80 0.05 0.05 3.02 2.99
reactants (HOCl/OCl- and CIOz-) and the products (Cl-, ClO,, and C103-). For the systems reported here, the ratio of C10,- to HOCl/OCl- consumed was 0.8-1.2 and the ratios of the products formed to the HOCl/OCl- consumed were 0.6-1.1,0.6-1.3, and 0-0.5, for Cl-/OCl-, ClO,-/OCl-, and ClO,/OCl-, respectively.
In view of the fact that the predominant species in the pH region of the experiments reported here are HOC1/
OC1- and C102-, and the proposal (vide infra) that chlorate ion is produced from the reaction between hypochlorous acid and chlorite ion (5, 13, 18, 19), reaction 2 has been rewritten as follows:
(4) By use of stoichiometric data such as that shown in Table I and in the supplementary material, the contribu- tion of reaction 1 to the overall reaction between the free
HClO,
+
HOC1-
C10,-+
C1-+
2H+V
0
.--..-.
... -..-... .~..(3
-.
7 0 9 10
PH
Figure 2. Contributions of reactions 1-3 for the consumption of HOCI/OCI- at various pH values.
chlorine added (Cl,/HOCl/OCl-) and CIOz- was calculated by assuming that chlorine dioxide was produced only by reaction 1 a t the initial stages of the experiment due to initial concentration gradients and the equilibration of the free chlorine (Cl,/HOCl) added as required by eq 3. After the contribution of reaction 1 for the consumption of chlorite ion from the initial concentration of sodium chlorite, [NaC10210, was subtracted, the remaining chlorite ion was assumed to be consumed by reaction 4. However, after subtraction of the contributions of reactions 1 and 4 from the reactants consumed and the products formed, there still remained some HOCl/OCl-, C1-, and C103-.
These remaining amounts of reactants and products cor- respond to the stoichiometry
(5) The contributions of reactions 1, 4, and 5 to the overall reaction changed with time during the course of the re- action: Reaction 1 contributed only at the initial stage of the overall reaction, while reaction 4 contributed over the whole range of the reaction. Reaction 5 did contribute a t the initial stage of the reaction. However, it was not clear whether this reaction continued to contribute at the latter stages of the reaction because of the magnitude of the experimental error near the end of the reaction. This tendency was observed for all systems studied (pH 6.4-10.0, [NaOCl]o/[NaCIOz], (mM/mM) = 3/6, 6/3, 3/3, and l / l ) .
Figure 2 shows the contributions of reactions 1 , 4 , and 5 integrated for the total course of the reaction to the overall reaction under various conditions. In the figure, the contributions were calculated based on the consump- tion of HOCl/OCl-. Thus, in the case of equal contribu- tions of reactions 4 and 5 to the formation of C103-, the contribution of reaction 5 in Figure 2 is calculated to be 3 times as large as that of reaction 4. The data shown in the figure have the following characteristics:
(1) Below pH 8, the contributions of reactions 1 and 5 to the overall reaction increase with decreasing pH. In the pH 8-10 region, the contributions of reactions 1 and 5 are very small and are almost constant.
( 2 ) The contribution of reaction 1 was 2-8 times larger
for a system of [NaOCl]o/[NaC102]o = 0.5 than that of [NaOCl]o/[NaCIOz]o = 2, while the contribution of reaction 5 was less for a system of [NaOCl]o/[NaC102]o = 0.5 than that of [NaOC1]O/[NaC102]o = 2. The contribution of reaction 4 was not largely affected by the ratio of the initial concentration of the reactants.
Rates of Reaction. In of all systems examined here, only a minor amount of C102 was formed during the initial
30C1-
-
C103-+
2C1-470 Environ. Sci. Technol., Vol. 25, No. 3, 1991
_-
20 40 60 80 (hours)
Time
Flgure 3. Typical third-order plots for the formation of chlorate ion with differing ratios of [NaOCI],/[NaCI02], where A = [NaOCI], and B = [NaCIO,],. The upper curve corresponds to pH 8.89, with the ratio [NaOCI],/[NaCIO,], = 1.91 mM15.06 mM. The lower curve is at pH 8.82 with [NaOCI],/[NaCIO,], = 4.99 mM12.27 mM.
stage of the reaction between HOCl/OCl- and C102-. The formation of C103- is the dominant reaction, as can be noted by the typical examples shown in Figure 1 and Table I. Thus, the kinetic analyses were carried out for the formation of C103- from data obtained in the latter part of each experiment.
In systems of [NaOCl],
>
[NaC10210, third-order plots, second order with respect to NaOCl and first order with respect to NaC102, are linear, as shown in the lower part of Figure 3. Thus, the rate law for the reaction becomes rate = h o b s [NaOC1]2[NaC102] (6) The third-order rate constant, hobs, was obtained directly from the slope of the linear plot. In a system with [NaO- Cl], f [NaC10210, as the course of the reaction proceeds the third-order plots deviate markedly from linearity, as is shown in the upper part of Figure 3. In this context, it should be noted that corresponding second-order plots (first order with respect to NaOCl and first order with respect to NaC10,) are also nonlinear.On the other hand, a Powell plot (30) for a system of [NaOCl], = [NaC10210 indicates that a third-order process is more likely than a second-order process. Thus, in such a system the third-order rate constant was obtained from the slope of the line a t the initial part of the plot.
The logarithmic values of the third-order rate constants thus obtained (h30bs) were plotted as a function of pH, as is shown in Figure 4. For these systems, the rate constants were calculated by using the actual concentrations of reactants in the system a t that specific point in time on the reaction curve. In the figure, it can be seen that the plot of log vs pH has a slope of 2 in the region of high pH and a slope of 1 in the region of low pH. The value
k3obs actually depends slightly on the concentrations of
reactants; for systems a t the same pH, k30bs was smaller for systems of larger concentrations of NaOCl (HOCl/
OC1-). The reciprocal of the rate constant is a linear function of the concentration of NaOCl (HOCl/OCl-) as shown in Figure 5. This is taken as direct evidence of the second-order role of NaOCl (HOCl/OCl-) in the overall reaction. This also means that the reaction must be first order with respect to the total concentration of NaCIOz (HC102/C102-).
6 7 8 9 10 11 12 13
PH
Figure 4. Plot of log kaobs as a function of pH for the formation of C103-. The values in the figures correspond to the concentration of HOC1 at the point in time when the individual values of the rate con- stants (k,,,,) were calculated.
0.5
0.4
0.2
0.1
0 1 2 3 4 5
[NaOCI], , rnM
Figure 5 . Plot of llk,,,, as a function of the concentration of NaOCI.
The open circles correspond to data at pH 9 in Figure 4 and the full circles are for the data at pH 8.89 in Figure 3. All of the data are corrected to pH 8.82 by using the empirical expression kcalcd = k,,,,[Hf]2. The values in the figure correspond to the concentration of HOC1 at the point in time when the individual values of the rate constants (k,,,,) were calculated.
Discussion
Stoichiometry. The concentration dependence of re- actions 1 , 4 , and 5 on the reactants as shown in Figure 2 is consistent with the stoichiometry of the reactions.
However, no detailed mechanistic information appears to be available in the literature for reactions 1 and 4. Our observation that the contribution of reaction 1 increases with decreasing p H values in the reaction between free chlorine and C102- in the p H 6.4-10.0 range is consistent with previous reports (8,20,21,31) that CIOz formation is dominant only a t low p H values.
On the other hand, we find that the stoichiometry of the reaction between HOCl/OCl- and C102- changes with time during the course of the reaction. This appears to be a result of the fact that reactions 1 and 5 occur only at the initial stages of the reaction while reaction 4 occurs con- tinuously during the whole course of the reaction.
Furthermore, the chlorine dioxide once produced cannot be the main origin of chlorate ion formed in the reaction,
since the rate of the reaction between chlorine dioxide and hypochlorous acid/ hypochlorite ion is slow when compared with the HOC1/C102- reaction in this pH range (13). This means that the production of chlorine dioxide and chlorate ion are independent of each other in solutions above p H 6. In the experiments reported here, no detectable chlorine dioxide formation was observed during the latter part of the reaction even in the presence of hypochlorous acid/
hypochlorite ion and chlorite ion, which were continuing to react to form chlorate ion at pH 6.4-10.0. This suggests that the observed CIOz formation at the initial stage of the reaction was caused by rapid reactions a t concentration gradients due to incomplete mixing and/or by the ad- ventitious presence of impurities such as metal ions ( 1 7 , 20, 21).
The observation of only chlorate ion formation was re- ported in 1987 by Werdehoff and Singer (18) and by Singer and O’Neil (19) for the chlorite ion/free chlorine (Le,, hypochlorous acid) reaction a t p H 7. Our results are consistent with their observations.
However, the results presented here are in contrast to the published facts (1 7, 20, 21) for the HOC1/HC102 re- action a t pH 15.0, where it is reported that the reaction produces both chlorine dioxide and chlorate ion. In this context, from the earlier reports, it is not clear whether the two products are formed in parallel or consecutive reactions. In none of the systems reported in the literature (9-21) has the time dependence of the formation of the products been measured during the course of the reaction a t pH 15.0. In order to clarify the stoichiometry of the true reaction between hypochlorous acid/hypochlorite ion and chlorite ion, it would be necessary to understand the time dependence of the contribution of the two reactions in “pure” systems at low pH values. No such data appear to be available.
In the study reported here, the C102 once produced gradually decreased with time during the course of the reaction, as shown in Figure 1. Since the glassware, the water, and the buffer were not prepared to be chlorine dioxide demand free as reported by Singer et al. (18,191, the very slow loss of chlorine dioxide could be a result of minor chlorine dioxide demand reactions with the buffer or the water itself or the loss might be explained by the following reactions (13):
(7) 2C1O2 2C102
+
HOCl+
H 2 0+ -
HzO C10,--
2C103-+
C102-+ +
C1- 2H++
3H+ (8)The reaction
3C102-
-
2C103-+
C1- (9)would also be required as a minor reaction path concurrent with reaction 4 for explaining the stoichiometric change of the overall reaction in the latter stage of the experiment.
Rates of Reaction. Mechanism for the Formation of Chlorate Ion. A third-order rate constant at pH 13.5 extrapolated from the data in Figure 4 is 3 X lo-’ M-2 s-’.
This value is l/jm as large as the value (1.5 X
lo4
M-2 s-l) calculated from the data reported by Lister (32-34) for the OCl-/ClO,- reaction in a “metal oxide free” system of 0.32 M NaOCl at 3.79 M ionic strength maintained with NaCl at 25 “C. The much smaller k value calculated for the formation of C103- in the system reported here suggests that the role of possible metal ion catalysis is even less than that reported by Lister. Moreover, the addition of 2.5 mM HgCl, did not alter the rate of formation of C103- at pH 7.87.The kinetic results in Figures 3-5 were interpreted in terms of the following mechanism.
HOCl
+
HC10, C1202+
H,O (10)k-1
c i 2 o ,
+
H O C ~2
~ 1 0 ~ -+
ci,+
H+ (11) where ClzOz is the same intermediate as was proposed by Taube and Dodgen ( 3 1 ) and others (8-10, 16, 17). This corresponds to the stoichiometric equation2HOC1+ HC10, F! C103-
+
Cl,+
H 3 0 + (12)The reaction rate is expressed as
klh2[HOC1]2[HC10z]
-d[HoC1l/dt = h-,
+
k,[HOCl] (13) Since the reaction was followed by the changes in total concentrations of hypochlorous acid/ hypochlorite ion, [NaOCl], and chlorous acid/chlorite ion, [NaClO,], eq 13 is transformed as follows by using [NaOCl] and [NaClO,]:-d[NaOCl] [H+] -
-
d t [H+]
+
K,klh2( [H+l
IH+]
+ K , )[NaOCll2( [H+][H+l +
K’ )[NaC102](14) where K , = 3.98 X (14, 15) and K’ = 1.76 X (35, 36) are the acid dissociation constants of HOCl and HClO,, respectively. By comparison of eq 14 with eq 6, the ob- served third-order rate constant becomes
In solutions with pH values above 6, since [H+]
<<
K’, the value of hobs from eq 6 transforms into eq 16:Under the conditions k-&,
>> k1 +
k2[NaOC1])[H+], the value of hobs is proportional to the square of the hy- drogen ion concentration, and when k-lKa<<
(kWl+
kz- [NaOCl])[H+], kobs is proportional to [H+]. These features correspond to the extrapolated solid line slopes drawn in Figure 4.If eq 15 is rewritten by taking the reciprocal of both sides of the equation, the following relationship obtains:
[NaOCll [H+]
+
K’(17) A linear relationship is obtained between l / k o b s and the concentration of NaOCl for each of the individual exper- iments reported here, as is shown in Figure 5. From the slope and the intercept of the plot, the following values were obtained: k, = (1.00 f 0.08) x lo5 M-l s-l and k-,/k,
= (2.29 f 0.15) x 10-5 M.
472 Environ. Sci. Technol., Vol. 25, No. 3, 1991
Substitution of these parameters into eq 17 results in third-order rate constants under various conditions of the experiments reported here. The calculated values are shown by solid lines in Figure 4. Agreement between the observed and calculated rate constants was satisfactory (Le., & l o % ) .
Equation 17 also explains why in systems of [NaOCl], 5 [NaClO&, the third-order plot deviates from linearity during the course of the reaction, as shown in the upper part of Figure 3 . The equation shows that hobs increases with time during the course of the reaction as a result of the consumption of hypochlorous acid/hypochlorite ion, or as a result of the denominator in the second term de- creasing to zero. Values of hobs for individual experiments as shown in the upper part of Figure 3, which were de- termined at various points in time, are also shown by full circles in Figure 5 . These results are in agreement with the earlier results.
All of the kinetic data obtained here were reproduced well ( & l o % ) by the reaction mechanism shown in eq 10 and 11. The mechanism differs from that proposed pre- viously (7-10, 16,17,20,21,31) in that, under mildly basic conditions, the C1,02 intermediate formed by reaction 10 is shown to react directly with HOCl to form chlorate ion.
Peintler, Nagypal, and Epstein (26) reported on the kinetics and mechanism of the reaction between chlorite ion and hypochlorous acid in the pH 5-6 range, where they presented evidence for the formation of the Cl2OZ inter- mediate and its subsequent reaction with excess chlorite ion to form chlorine dioxide. Our results are consistent with their model and agree quantitatively within 1 order of magnitude. This is considered to be very good consid- ering the marked changes in pH and ionic strength for the total set of experiments and the fact that they postulated a mechanism for the formation of both chlorine dioxide and chlorate ion although only the production of chlorine dioxide was determined experimentally. In addition, we also show experimental evidence for the additional reaction of hypochlorous acid with the C1202 intermediate to form chlorate ion directly, which has not been reported previ- ously.
In the high-pH regions, all evidence (32-34, 37-39) suggests that especially a t high temperatures the direct reaction
C10*-
+ oc1- - c10,- + c1- (18)
is primarily responsible for the relatively slow production of chlorate ion. This reaction and its slow rate of pro- duction of C103- is consistent with the results presented here.
Mechanism of the Formation of Clop Chlorine di- oxide was produced only during the short time between the initial mixing of reactants and the time when the first measurement was carried out on the actual concentrations of the reactants and products in the reaction mixture. We suggest that the C102 was formed as a result of concen- tration gradients or because of the adventitious presence of catalytic metal ion impurities. If metal ions were re- sponsible for the production of C10, as catalysts of the reaction between HOCl/OCl- and CIOz-, the time depen- dence of the C l 0 2 formation may be understood in terms of precipitation of the catalysts shortly after mixing the reactants due to the change in pH. Only new experiments will clarify this hypothesis.
In any case, the initial formation of small amounts of ClOz in the pH 6-10 region does raise questions with re- spect to the origin of ClO, a t other p H regions. In other words, is it possible that such adventitious production of C102 is also occurring to some extent in the lower p H
region as well? In this context, reaction 5 was observed primarily a t the first stages of the overall reaction when ClO, was also being produced, which suggests that reaction 5 is also catalyzed by impurities present a t the initiation of the reaction.
Extrapolation of the fitted equation to pH 0.7 (0.2 M HC104) results in a calculated half-life for the production of CIOz of a t least 100 times less than that reported by Emmenegger and Gordon (8). This strongly suggests that the chlorite ion/hypochlorous ion reaction is far too slow to account for chlorine dioxide production in the low pH region-but that rather, the chlorine dioxide is produced by the corresponding chlorine/ chlorous acid reaction.
However, only additional experiments with extremely pure starting reagents will determine the remaining details of the differences between the reactions of chlorite ion/
chlorous acid with hypochlorous acid/hypochlorite ion and chlorine itself.
The use of chlorine dioxide demand glassware, water, and buffer as reported by Singer et al. (18,19) is one way to minimize the uncertainty; however, only additional kinetic studies in the low-pH region with “impurity-free’’
systems will completely uncover the detailed mechanism of CIOz formation under conditions such as are reported here.
Supplementary Material Available
Concentration vs time data for HOCl, ClO?, CIOz, C103-, and Cl- measurements in the data fitting (9 pages) will appear following these pages in the microfilm edition of this volume of the journal.
Photocopies of the supplementary material from this paper or microfiche (105 X 148 mm, 24X reduction, negatives) may be obtained from Microforms Office, American Chemical Society, 1155 16th St., N.W., Washington, DC 20036. Full bibliographic citation (journal, title of article, authors’ names, inclusive pagi- nation, volume number, and issue number) and prepayment, check or money order for $19.00 for photocopy ($21.00 foreign) or $10.00 for microfiche ($11.00 foreign), are required.
Chlorate, 14866-68-3; hypochlorous acid, 7790-92-3; chlorite, 14998-27-7.
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Geostatistical Modeling of Dissolved Oxygen Distribution in Estuarine Systems
Donato Posat and Mario E. Rossi”8t
IRMA, CNR, Universiti degli Studi di Bari, 70125 Bari, Italy, and Fluor Daniel Inc., 10 Twin Dolphin Drive, Redwood City, California 94065
The probabilistic random function model is used in geostatistics to infer the attribute under study a t unsam- pled locations. In many earth sciences applications, sparse information and incomplete sampling are not uncommon.
This problem sometimes can be approached with an ap- propriate definition of the stationary random function model being used. In spatial statistics this decision is usually influenced by practical factors, such as availability and distribution of the samples. This paper describes a procedure that trades the third dimension for a larger number of samples in the two-dimensional space. This allows for a better characterization of the distribution of dissolved oxygen within the Mar Piccolo of Taranto, Italy.
Introduction
T o accurately assess the risk and plan the remediation of contaminated estuarine systems, it is necessary to model the spatial distribution of the relevant physical and chemical variables within that system. More often than not, incomplete knowledge of all the processes involved prevents the analyst from using deterministic models. In addition, there are usually too few and too sparse samples to aid in the modeling process. In such cases, a proba- bilistic model that takes into account the uncertainty as- sociated with the estimates is needed. Geostatistics is the name given to a toolbox of statistical techniques that deal with data correlated in space. This relatively new branch of statistics has gained widespread acceptance within the mining, petroleum, and, lately, hydrogeology fields.
Geostatistical techniques are based on the probabilistic concept of a random function model ( I ) , built under the following assumptions: (i) the data are statistically ho-
t Universitd degli Studi di Bari.
*Fluor Daniel, Inc.
mogeneous (stationary), and (ii) the statistics inferred from the samples are representative of the global population.
The spatial dependence between two variables at different locations within the area of interest is inferred and mod- eled from the sample data. A correlation function (either a variogram, covariance, or correlogram) is expressed as a function of the distance between samples. “Inference”
of the correlation function implies obtaining from the samples a few experimental points, which are then modeled with an analytical equation. This mathematical model thus measures how “close” two samples are in space and uses this information to interpolate values a t unknown locations by use of a generalized least-squares algorithm ( 2 ) called kriging (ref 3, pp 303-4431,
In practice, and as is usually the case in any data-based methodology, geostatistical analysis is adversely affected by lack of information. In particular, obtaining an ex- perimental variogram that describes the spatial variability of the data can be extremely difficult if there are not enough samples available. This is so because each ex- perimental variogram value requires a minimum number of sample pairs for the variogram function to be stable and statistically significant (ref 3, pp 194).
The problems associated with inference of statistical moments of a random function model have been discussed by several authors (see refs 4-6 for environmental appli- cations). Any analysis that requires statistical inference will suffer from sparse information.
The study presented in this paper deals with dissolved oxygen (DO) measurements, taken a t 16 stations on the Mar Piccolo of Taranto, Italy, on March 19, 1986, over an area of approximately 3000 m by 3800 m. The basin is made up of two bays, which communicate a t the Punta Penna and Punta Pizzone (Figure 1). The first bay, which is the focus of this study, is connected with the Mar Grande and the Ionian Sea by two channels: Canale Porta
474 Environ. Sci. Technol., Vol. 25, No. 3, 1991 0013-936X/91/0925-0474$02.50/0 0 1991 American Chemical Society
